Finally, we argue that from the perspective of a single player (take Player 1 as an example), our algorithm is also rational, in the sense that it allows Player 1 to converge to the best response to her opponent if Player 2 is not applying our algorithm but instead uses an arbitrary stationary policy.The rationality defined by [1]} requires that the learner converges to the best response as long as the opponent converges to a stationary policy. While our algorithm does handle this case, as a proof of concept, we only consider the simpler scenario where the opponent simply uses a stationary policy.
We show this single-player-perspective version in algo: main alg single, where Player 1 still follows the updates eq: update 1, eq: update 2, and eq: update 5, while \(y_t\)  is fixed to a stationary policy \(y\)  used by Player 2.
